{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quadrature\n",
    "\n",
    "This is a notebook that illustrates differences in the quadrature methods which are central to the evaluation of\n",
    "\n",
    "$$\n",
    "\\int_0^{\\pi} f(\\theta) \\sin \\theta \\; \\mathrm{d}\\theta = \\int_{-1}^{1} f(\\cos \\theta) \\; \\mathrm{d}\\cos \\theta.\n",
    "$$\n",
    "\n",
    "Quadrature is used to compute the projection onto the associated Legendre functions in `torch-harmonics`.\n",
    "\n",
    "In order to illustrate how interpolation and quadrature affect the error in the computation of the SHT, this notebook contains example for both errors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\lixia\\AppData\\Local\\anaconda3\\envs\\paddle310\\lib\\site-packages\\paddle\\utils\\cpp_extension\\extension_utils.py:686: UserWarning: No ccache found. Please be aware that recompiling all source files may be required. You can download and install ccache from: https://github.com/ccache/ccache/blob/master/doc/INSTALL.md\n",
      "  warnings.warn(warning_message)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import paddle\n",
    "import scipy\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_theta = 80"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append(\"..\")\n",
    "from paddle_harmonics.quadrature import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test interpolation\n",
    "\n",
    "we first assess the interpolation onto the quadrature nodes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# interpolation - careful - this breaks if points align (for non-periodic signals)\n",
    "def interpolate(t, tq, f):\n",
    "    j = np.searchsorted(t, tq) - 1\n",
    "    d = paddle.to_tensor((tq - t[j]) / np.diff(t)[j])\n",
    "    j = paddle.to_tensor(j)\n",
    "    interp = paddle.lerp(paddle.to_tensor(f[j]), paddle.to_tensor(f[j + 1]), d)\n",
    "    # interp = f[j] + (f[j+1] - f[j]) * (tq - t[j]) / np.diff(t)[j]\n",
    "    # print(d)\n",
    "    # print(f[j+1] - f[j])\n",
    "    # print(j)\n",
    "    return interp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "cost_lg, wlg = legendre_gauss_weights(n_theta, -1, 1)\n",
    "# cost_lg, wlg = lobatto_weights(n_theta, -1, 1)\n",
    "tq = np.flip(np.arccos(cost_lg))\n",
    "teq = np.linspace(0, np.pi, n_theta, dtype=np.float64)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(teq, '.')\n",
    "plt.plot(tq, '.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "test interpolation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "f = lambda t : np.cos(4*t)\n",
    "# f = lambda t : 1 / (1 + 25 * (2*(t-np.pi/2)/np.pi)**2)\n",
    "# f = lambda t : 1 / (1 + 25 * np.cos(t)**2)\n",
    "# f = lambda t : t**5 - 3*t**2 - 2*t + 1.0\n",
    "\n",
    "interp = interpolate(teq, tq, f(teq))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Tensor(shape=[80], dtype=float64, place=Place(gpu:0), stop_gradient=True,\n",
       "       [0.99051621, 0.96017247, 0.90654557, 0.83090023, 0.73507102, 0.62138695,\n",
       "        0.49261122, 0.35187340, 0.20259315, 0.04839723, -0.10696858, -0.25973031,\n",
       "        -0.40617737, -0.54275253, -0.66613820, -0.77333689, -0.86174389, -0.92921053,\n",
       "        -0.97409622, -0.99530837, -0.99232890, -0.96522689, -0.91465698, -0.84184357,\n",
       "        -0.74855128, -0.63704220, -0.51002113, -0.37057012, -0.22207379, -0.06813728,\n",
       "        0.08750110, 0.24106052, 0.38880936, 0.52715572, 0.65273465, 0.76248985,\n",
       "        0.85374796, 0.92428359, 0.97237355, 0.99683884, 0.99683884, 0.97237355,\n",
       "        0.92428359, 0.85374796, 0.76248985, 0.65273465, 0.52715572, 0.38880936,\n",
       "        0.24106052, 0.08750110, -0.06813728, -0.22207379, -0.37057012, -0.51002113,\n",
       "        -0.63704220, -0.74855128, -0.84184357, -0.91465698, -0.96522689, -0.99232890,\n",
       "        -0.99530837, -0.97409622, -0.92921053, -0.86174389, -0.77333689, -0.66613820,\n",
       "        -0.54275253, -0.40617737, -0.25973031, -0.10696858, 0.04839723, 0.20259315,\n",
       "        0.35187340, 0.49261122, 0.62138695, 0.73507102, 0.83090023, 0.90654557,\n",
       "        0.96017247, 0.99051621])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "interp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.        ,  0.98737534,  0.94982013,  0.88828261,  0.80431657,\n",
       "        0.70004207,  0.578092  ,  0.4415455 ,  0.29385027,  0.13873553,\n",
       "       -0.01988219, -0.1779979 , -0.33161928, -0.4768675 , -0.61007515,\n",
       "       -0.72787881, -0.82730403, -0.90584039, -0.9615049 , -0.99289207,\n",
       "       -0.9992094 , -0.98029737, -0.9366335 , -0.86932027, -0.78005731,\n",
       "       -0.67109843, -0.54519477, -0.40552532, -0.25561663, -0.0992538 ,\n",
       "        0.05961513,  0.21697881,  0.36886392,  0.51143548,  0.64109364,\n",
       "        0.75456462,  0.84898336,  0.92196585,  0.97166934,  0.99683884,\n",
       "        0.99683884,  0.97166934,  0.92196585,  0.84898336,  0.75456462,\n",
       "        0.64109364,  0.51143548,  0.36886392,  0.21697881,  0.05961513,\n",
       "       -0.0992538 , -0.25561663, -0.40552532, -0.54519477, -0.67109843,\n",
       "       -0.78005731, -0.86932027, -0.9366335 , -0.98029737, -0.9992094 ,\n",
       "       -0.99289207, -0.9615049 , -0.90584039, -0.82730403, -0.72787881,\n",
       "       -0.61007515, -0.4768675 , -0.33161928, -0.1779979 , -0.01988219,\n",
       "        0.13873553,  0.29385027,  0.4415455 ,  0.578092  ,  0.70004207,\n",
       "        0.80431657,  0.88828261,  0.94982013,  0.98737534,  1.        ])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(teq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plt.plot(teq, f(teq), '.-', label=\"reference\")\n",
    "plt.plot(tq, f(tq), '.-', label=\"reference\")\n",
    "# plt.plot(tq, interp, '.-', label=\"interpolated\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test quadrature with associated Legendre polynomials\n",
    "\n",
    "let us test different quadrature modes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def precompute_legpoly(m_max, l_max, x):\n",
    "    \"\"\"\n",
    "    Computes the values of P^m_n(\\cos \\theta) at the positions specified by x (theta)\n",
    "    The resulting tensor has shape (m_max, l_max, len(x))\n",
    "    \"\"\"\n",
    "\n",
    "    # compute the tensor P^m_n:\n",
    "    pct = np.zeros((m_max, l_max, len(x)), dtype=np.float64)\n",
    "\n",
    "    sinx = np.sin(x)\n",
    "    cosx = np.cos(x)\n",
    "\n",
    "    a = lambda m, l: np.sqrt((4*l**2 - 1) / (l**2 - m**2))\n",
    "    b = lambda m, l: -1 * np.sqrt((2*l+1)/(2*l-3)) * np.sqrt(((l-1)**2 - m**2)/(l**2 - m**2))\n",
    "\n",
    "    # start by populating the diagonal and the second higher diagonal\n",
    "    amm = np.sqrt( 1. / (4 * np.pi) )\n",
    "    pct[0,0,:] = amm\n",
    "    pct[0,1,:] = a(0, 1) * cosx * amm\n",
    "    for m in range(1, min(m_max, l_max)):\n",
    "        pct[m,m,:] = -1*np.sqrt( (2*m+1) / (2*m) ) * pct[m-1,m-1,:] * sinx\n",
    "        if m + 1 < l_max:\n",
    "            pct[m,m+1,:] = a(m, m+1) * cosx * pct[m,m,:]\n",
    "\n",
    "    # fill the remaining values on the upper triangle\n",
    "    for m in range(0, m_max):\n",
    "        for l in range(m+2, l_max):\n",
    "            pct[m,l,:] = a(m,l) * cosx * pct[m,l-1,:] + b(m,l) * pct[m,l-2,:]\n",
    "\n",
    "    return paddle.to_tensor(pct)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us plot the Legendre polynomials:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\lixia\\AppData\\Local\\Temp\\ipykernel_27764\\3670297094.py:8: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
      "  fig.show()\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = 0\n",
    "\n",
    "pct = np.sqrt(2 * np.pi) * precompute_legpoly(n_theta, n_theta, teq)\n",
    "\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "for l in range(6):\n",
    "    ax.plot(np.cos(teq), pct.numpy()[0, l])\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def project(t, w, f, mmax=None):\n",
    "    m = 0\n",
    "    if mmax == None:\n",
    "        mmax = len(t)\n",
    "\n",
    "    weights = paddle.to_tensor(w)\n",
    "    pct = np.sqrt(2 * np.pi) * precompute_legpoly(mmax, mmax, t)\n",
    "    weights = paddle.einsum('mlk,k->mlk', pct, weights)\n",
    "\n",
    "    proj = paddle.einsum('...k,lk->...l', paddle.to_tensor(f), weights[m])\n",
    "    rec = paddle.einsum('...l, lk->...k', proj, pct[m] )\n",
    "    return rec"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "let us compare the accuracy of the different projection methods:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.linspace(0, np.pi, n_theta)\n",
    "plt.plot(t, f(t), label=\"reference\")\n",
    "\n",
    "for quadrature in [legendre_gauss_weights, lobatto_weights, clenshaw_curtiss_weights, fejer2_weights]:\n",
    "    cost, wq = quadrature(n_theta, -1, 1)\n",
    "    tq = np.flip(np.arccos(cost))\n",
    "\n",
    "    out = project(tq, wq, f(tq))\n",
    "\n",
    "    plt.plot(tq, out.numpy(), '.-', label=quadrature.__name__)\n",
    "\n",
    "plt.legend(loc='lower left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for quadrature in [legendre_gauss_weights, lobatto_weights, clenshaw_curtiss_weights]:\n",
    "    cost, wq = quadrature(n_theta, -1, 1)\n",
    "    tq = np.flip(np.arccos(cost))\n",
    "\n",
    "    out = project(tq, wq, f(tq))\n",
    "    # print(np.abs(out - f(tq)))\n",
    "\n",
    "    plt.semilogy(tq, out.numpy() - f(tq), '.-', label=quadrature.__name__)\n",
    "\n",
    "plt.legend(loc='lower left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us now add interpolation into the mix to evaluate performance with interpolation taken into account. For this particular case, we will assume that the data is given to us on an equidistant grid."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.linspace(0, np.pi, n_theta)\n",
    "ref = f(t)\n",
    "plt.plot(t, ref, label=\"reference\")\n",
    "\n",
    "for quadrature in [legendre_gauss_weights, lobatto_weights, clenshaw_curtiss_weights]:\n",
    "    cost, wq = quadrature(n_theta, -1, 1)\n",
    "    tq = np.flip(np.arccos(cost))\n",
    "\n",
    "    if quadrature == lobatto_weights or quadrature == legendre_gauss_weights:\n",
    "        f_interp = interpolate(t, tq, ref)\n",
    "        mmax = len(tq)\n",
    "    else:\n",
    "        f_interp = ref\n",
    "        mmax = len(tq)\n",
    "\n",
    "    out = project(tq, wq, f_interp, mmax=mmax)\n",
    "\n",
    "    plt.plot(tq, out.numpy(), '.-', label=quadrature.__name__)\n",
    "\n",
    "plt.legend(loc='lower left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "again, let us plot the overall error, this time including the interpolation error:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.linspace(0, np.pi, n_theta)\n",
    "ref = f(t)\n",
    "\n",
    "fig, ax = plt.subplots(2, 1)\n",
    "\n",
    "for quadrature in [legendre_gauss_weights, lobatto_weights, clenshaw_curtiss_weights]:\n",
    "    cost, wq = quadrature(n_theta, -1, 1)\n",
    "    tq = np.flip(np.arccos(cost))\n",
    "\n",
    "    if quadrature == lobatto_weights or quadrature == legendre_gauss_weights:\n",
    "        f_interp = interpolate(t, tq, ref).numpy()\n",
    "        mmax = len(tq)\n",
    "    else:\n",
    "        f_interp = ref\n",
    "        mmax = len(tq)\n",
    "\n",
    "    out = project(tq, wq, f_interp, mmax=mmax)\n",
    "\n",
    "    ax[0].semilogy(tq, out.numpy() - f(tq), '.-', label=quadrature.__name__)\n",
    "    ax[1].semilogy(tq, f_interp - f(tq), '.-', label=quadrature.__name__)\n",
    "\n",
    "ax[0].set_title(\"Projection error after interpolation\")\n",
    "ax[1].set_title(\"Interpolation error\")\n",
    "# ax[0].legend(loc='lower left')\n",
    "# ax[1].legend(loc='lower left')\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can see that the interpolation dominates when we interpolate the solution. For this reason, it is reasonable t choose Clenshaw-Curtiss quadrature in scenarios where we expect the interpolation error to dominate."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "paddle310",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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